Logic, Language, Information, and Computation

This work presents an algorithmic reduction of the word problem for recursively presented groups to the word problem for recursively presented quandles. The faithfulness of the reduction follows from the conjugation quandle construction on groups. It follows that the word problem for recursively presented quandles is not effectively computable, in general. This article also demonstrates that a recursively presented quandle can be encoded as a recursively presented rack. Hence the word problem for recursively presented racks is also not effectively computable.

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